Gravitational potentials and forces in the Lattice Universe: a slab

Abstract

We study the effect of the slab topology $T\times R\times R$ of the Universe on the form of gravitational potentials and forces created by point-like masses. We obtain two alternative forms of solutions: one is based on the Fourier series expansion of the delta function using the periodical property along the toroidal dimension, and another one is derived by direct summation of solutions of the Helmholtz equation for the source particle and all its images. The latter one takes the form of the sum of Yukawa-type potentials. We demonstrate that for the present Universe the latter solution is preferable for numerical calculations since it requires less terms of the series to achieve the necessary precision.

arXiv commentThis is a preprint of an article published in the European Physical Journal Plus. The final authenticated version is available online at: https://doi.org/10.1140/epjp/s13360-021-01139-y

References in corpus (16)

• First-order Cosmological Perturbations Engendered by Point-like Masses
• Constraints on the Topology of the Universe: Extension to General Geometries
• Constraints on the topology of the Universe derived from the 7-year WMAP data
• The Topology and Size of the Universe from CMB Temperature and Polarization Data
• The Topology and Size of the Universe from the Cosmic Microwave Background
• The study of topology of the universe using multipole vectors
• The Shape and Topology of the Universe
• Cosmic screening of the gravitational interaction
• Scalar and vector perturbations in a universe with discrete and continuous matter sources
• Topology beyond the horizon: how far can it be probed?
• On Topological Modifications of Newton's Law
• Cosmological law of universal gravitation
• Zero average values of cosmological perturbations as an indispensable condition for the theory and simulations
• Lattice Universe: examples and problems
• Topology of the Universe: background and recent observational approaches
• Topology of the Universe